What is the ruling on the ablution of one who cuts his nails, and is it permissible to cut them before the ritual bath for major impurity (janabah)?
Cutting nails does not invalidate ablution, and it is permissible to cut them before the ritual bath for major impurity. And Allah the Almighty knows best.
Is it permissible for a sick person to pray while sitting on a chair?
All perfect praise be to Allah, The Lord of the Worlds It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.
Is it obligatory to make up all missed prayers?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Making up missed prayers (qaḍāʾ) is a sharʿī obligation, established by the practice of the Prophet ﷺ himself — when the disbelievers preoccupied him on the Day of the Trench and he missed the ʿAṣr prayer, he made it up afterward. This is further affirmed by the ḥadīth: "Fulfil what you owe to Allah, for Allah is most deserving of being fulfilled." (Reported by al-Bukhārī.)
Accordingly, a person who has missed prayers should set aside his voluntary and Sunnah prayers and replace them with make-up prayers in their stead. There is no objection to making up one missed prayer alongside each obligatory prayer that is performed — praying the equivalent missed prayer together with each current obligatory prayer as a practical and manageable way of gradually clearing one's debt of missed prayers. And Allah the Almighty knows best.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.